ISO 31-0 is the introductory part of
international standard ISO 31
ISO 31 ( Quantities and units, International Organization for Standardization, 1992) is a superseded international standard concerning physical quantities, units of measurement, their interrrelationships and their presentation. It was revised and ...
on
quantities
Quantity or amount is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a unit ...
and
units
Unit may refer to:
Arts and entertainment
* UNIT, a fictional military organization in the science fiction television series ''Doctor Who''
* Unit of action, a discrete piece of action (or beat) in a theatrical presentation
Music
* Unit (album), ...
. It provides guidelines for using physical quantities, quantity and unit symbols, and coherent unit systems, especially the
SI. It is intended for use in all fields of science and technology and is augmented by more specialized conventions defined in other parts of the
ISO 31
ISO 31 ( Quantities and units, International Organization for Standardization, 1992) is a superseded international standard concerning physical quantities, units of measurement, their interrrelationships and their presentation. It was revised and ...
standard. ISO 31-0 was withdrawn on 17 November 2009. It is superseded by
ISO 80000-1. Other parts of ISO 31 have also been withdrawn and replaced by parts of
ISO 80000
ISO 80000 or IEC 80000 is an international standard introducing the International System of Quantities (ISQ).
It was developed and promulgated jointly by the International Organization for Standardization (ISO) and the International Electrote ...
.
Scope
ISO 31 covers
physical quantities
A physical quantity is a physical property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ' Numerical value ' and a ' Unit '. For exam ...
used for the quantitative description of physical phenomena. The presentation here is a summary of some of the detailed guidelines and examples given in the standard.
Quantities and units
Physical quantities can be grouped into mutually comparable categories. For example, length, width, diameter and wavelength are all in the same category, that is they are all ''quantities of the same kind''. One particular example of such a quantity can be chosen as a reference quantity, called the ''unit'', and then all other quantities in the same category can be expressed in terms of this unit, multiplied by a number called the ''numerical value''. For example, if we write
: the wavelength is ''λ'' = 6.982 × 10
−7 m
then "''λ''" is the symbol for the physical quantity (wavelength), "m" is the symbol for the unit (metre), and "6.982 × 10
−7" is the numerical value of the wavelength in metres.
More generally, we can write
: ''A'' = ⋅
'A''
where ''A'' is the symbol for the quantity, symbolizes the numerical value of ''A'', and
'A''represents the corresponding unit in which ''A'' is expressed here. Both the numerical value and the unit symbol are factors, and their product is the quantity. A quantity itself has no inherent particular numerical value or unit; as with any product, there are many different combinations of numerical value and unit that lead to the same quantity (e.g., ''A'' = 300 ⋅ m = 0.3 ⋅ km = ...). This ambiguity makes the and
'A''notations useless, unless they are used together.
The value of a quantity is independent of the unit chosen to represent it. It must be distinguished from the numerical value of the quantity that occurs when the quantity is expressed in a particular unit. The above curly-bracket notation could be extended with a unit-symbol index to clarify this dependency, as in
m = 6.982 × 10
−7 or equivalently
nm = 698.2. In practice, where it is necessary to refer to the numerical value of a quantity expressed in a particular unit, it is notationally more convenient to simply divide the quantity through that unit, as in
: ''λ''/m = 6.982 × 10
−7
or equivalently
: ''λ''/nm = 698.2.
This is a particularly useful and widely used notation for labelling the axes of graphs or for the headings of table columns, where repeating the unit after each numerical value can be typographically inconvenient.
Typographic conventions
Symbols for quantities
* Quantities are generally represented by a symbol formed from single letters of the Latin or Greek alphabet.
* Symbols for quantities are set in
italic type
In typography, italic type is a cursive font based on a stylised form of calligraphic handwriting. Owing to the influence from calligraphy, italics normally slant slightly to the right. Italics are a way to emphasise key points in a printed ...
, independent of the type used in the rest of the text.
* If in a text different quantities use the same letter symbol, they can be distinguished via subscripts.
* A subscript is only set in italic type if it consists of a symbol for a quantity or a variable. Other subscripts are set in upright (
roman
Roman or Romans most often refers to:
*Rome, the capital city of Italy
*Ancient Rome, Roman civilization from 8th century BC to 5th century AD
*Roman people, the people of ancient Rome
*'' Epistle to the Romans'', shortened to ''Romans'', a lette ...
) type. For example, write ''V''
n for a "nominal volume" (where "n" is just an abbreviation for the word "nominal"), but write ''V
n'' if ''n'' is a running index number.
Names and symbols for units
* If an internationally standardized symbol exists for a unit, then only that symbol should be used. See the
SI articles for the list of standard symbols defined by the International System of Units. Note that the distinction between uppercase and lowercase letters is significant for SI unit symbols. For example, "k" is the prefix kilo and "K" stands for the unit kelvin. The symbols of all SI units named after a person or a place start with an uppercase letter, as do the symbols of all prefixes from mega on upwards. All other symbols are lowercase; the only exception is
litre
The litre (international spelling) or liter (American English spelling) (SI symbols L and l, other symbol used: ℓ) is a metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metre (m3 ...
, where both l and L are allowed. However, it is stated that the CIPM will examine whether one of the two may be suppressed.
* Symbols for units should be printed in an upright (
roman
Roman or Romans most often refers to:
*Rome, the capital city of Italy
*Ancient Rome, Roman civilization from 8th century BC to 5th century AD
*Roman people, the people of ancient Rome
*'' Epistle to the Romans'', shortened to ''Romans'', a lette ...
) typeface.
Numbers
See Sect. 3.3 of the Standard text.
* Numbers should be printed in upright (
roman
Roman or Romans most often refers to:
*Rome, the capital city of Italy
*Ancient Rome, Roman civilization from 8th century BC to 5th century AD
*Roman people, the people of ancient Rome
*'' Epistle to the Romans'', shortened to ''Romans'', a lette ...
) type.
* ISO 31-0 (after Amendment 2) specifies that "the
decimal sign
A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form (e.g., "." in 12.45). Different countries officially designate different symbols for use as the separator. The ch ...
is either the comma on the line or the point on the line". This follows resolution 10 of the 22nd
CGPM, 2003.
: For example, one divided by two (one half) may be written as 0.5 or 0,5.
* Numbers consisting of long sequences of digits can be made more readable by separating them into groups, preferably groups of three, separated by a small space. For this reason, ISO 31-0 specifies that such groups of digits should never be separated by a comma or point, as these are reserved for use as the decimal sign.
: For example, one million (1000000) may be written as 1 000 000.
* For numbers whose magnitude is less than 1, the decimal sign should be preceded by a zero.
* The multiplication sign is either a cross or a half-height dot, though the latter should not be used when the dot is the decimal separator.
Expressions
* Unit symbols follow the numerical value in the expression of a quantity.
* Numerical value and unit symbol are separated by a space. This rule also applies to the symbol "°C" for degrees Celsius, as in "25 °C", and to the
percent sign
The percent sign (sometimes per cent sign in British English) is the symbol used to indicate a percentage, a number or ratio as a fraction of 100. Related signs include the permille (per thousand) sign and the permyriad (per ten thousand) ...
, as in "10 %". The only exceptions are the symbols for the units of plane angle: degree, minute of arc, and second of arc – which follow the numerical value without a space in between (for example "30°").
* Where quantities are added or subtracted, parenthesis can be used to distribute a unit symbol over several numerical values, as in
: ''T'' = 25 °C − 3 °C = (25 − 3) °C
: ''P'' = 100 kW ± 5 kW = (100 ± 5) kW
: (but not: 100 ± 5 kW)
: ''d'' = 12 × (1 ± 10
−4) m
* Products can be written as ''ab'', ''a b'', ''a''⋅''b'', or ''a''×''b''. The sign for multiplying numbers is a cross (×) or a half-height dot (⋅). The cross should be used adjacent to numbers if a dot on the line is used as the decimal separator, to avoid confusion between a decimal dot and a multiplication dot.
* Division can be written as
, ''a''/''b'', or by writing the product of ''a'' and ''b''
−1, for example ''a''⋅''b''
−1. Numerator or denominator can themselves be products or quotients, but in this case, a solidus (/) should not be followed by a multiplication sign or division sign on the same line, unless parentheses are used to avoid ambiguity.
Mathematical signs and symbols
A comprehensive list of internationally standardized mathematical symbols and notations can be found in
ISO 31-11.
See also
*
ISO 31
ISO 31 ( Quantities and units, International Organization for Standardization, 1992) is a superseded international standard concerning physical quantities, units of measurement, their interrrelationships and their presentation. It was revised and ...
*
ISO 1000
International standard ISO 1000 (''SI units and recommendations for the use of their multiples and of certain other units'', International Organization for Standardization, 1992) is the ISO standard describing the International System of Units ( ...
*
SI
*
ISO 31-11
*
ISO 80000
ISO 80000 or IEC 80000 is an international standard introducing the International System of Quantities (ISQ).
It was developed and promulgated jointly by the International Organization for Standardization (ISO) and the International Electrote ...
,
ISO 80000-1
References
Bibliography
*
International standard ISO 31-0: Quantities and units — Part 0: General principles.
International Organization for Standardization
The International Organization for Standardization (ISO ) is an international standard development organization composed of representatives from the national standards organizations of member countries. Membership requirements are given in Art ...
, Geneva, 1992.
SI brochure Bureau International des Poids et Mesures.
* .
* I. M. Mills and W. V. Metanomski
Interdivisional Committee on Nomenclature and Symbols,
IUPAC
The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
, December 1999.
* B. N. Taylor and A. Thompson
The International System of Units (SI) NIST Special Publication 330. US National Institute of Standards and Technology, 2008.
* A. Thompson and B. N. Taylor
NIST Special Publication 811. US National Institute of Standards and Technology, 2008.
US
National Institute of Standards and Technology
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical s ...
, 1998.
{{ISO standards
#00031-0
1992 introductions